# How do people know that their experiment follows a gamma distribution?

I am currently taking a Probability and Statistics course and learning the gamma function. Problems are usually phrased like "A group of scientists did x experiment and it followed a gamma distribution (...)" but I am wondering how do they know? Especially since the gamma function shape varies a lot depending on the values.

• Gamma distribution emerges naturally in phenomena that follow the laws of the Poisson process.
– YJT
Oct 30, 2020 at 14:01
• @YJT so you mean that whenever we have an experiment with an event that happens on average x times every y interval then gamma distribution will occur naturally? Oct 30, 2020 at 14:05
• The same way you can use a linear regression model and take a high correlation coefficient to suspect with reasonable certainty that the linear equation models the true data.
– user694818
Oct 30, 2020 at 14:06
• @MatthewDaly the case you are talking about is way simpler imho, do they first suspect it is a gamma distribution based on the shape and try to find values of alpha and beta by trial and error? Oct 30, 2020 at 14:10
• That's not exactly the definition, but yes. For example, we know that radioactive elements emerge particles according to a Poisson process with some parameters. The time between turning on the equipment and detecting the first particle follows an exponential distribution. The time until the $n$th particle is already gamma (gamma=sum of exp).
– YJT
Oct 30, 2020 at 14:12